Addition of virtual bass in the frequency domain

ABSTRACT

Provided are, among other things, systems, methods and techniques for processing an audio signal to add virtual bass. In one representative embodiment, an apparatus includes: (a) an input line that inputs an original audio signal; (b) a transform module that transforms the original audio signal into a set of frequency components; (c) a bass extraction filter that extracts a bass portion of such frequency components; (d) an estimator that estimates a fundamental frequency of a bass sound within such bass portion; (e) a frequency translator that shifts the bass portion by a frequency that is an integer multiple of the fundamental frequency estimated by the estimator, thereby providing a virtual bass signal; (f) an adder having (i) inputs coupled to the original audio signal and to the virtual bass signal and (ii) an output; and (g) an audio output device coupled to the output of the adder.

FIELD OF THE INVENTION

The present invention pertains, among other things, to systems, methodsand techniques for processing an audio signal in order to provide alistener with a stronger bass impression or, in other words, to add“virtual bass” to the audio signal, e.g., so that it can be playedthrough a speaker or other audio-output device that does not have goodbass production characteristics.

BACKGROUND

The advent of flat-panel televisions and mobile devices has acceleratedthe widespread use of small loudspeakers, which are well-known for theirpoor bass (i.e., low-frequency) performance. This characteristictypically places them in a disadvantageous position because a listener'soverall impression of sound quality is strongly influenced by bassperformance. It is, therefore, highly desirable to improve perceivedbass performance, particularly with respect to devices that incorporatesmall loudspeakers.

A conventional approach to boosting bass performance is to simplyamplify the low-frequency part of the audio spectrum, thereby making thebass sounds louder. However, the effectiveness of such an approach issignificantly limited because small speakers typically have poorefficiency when converting electrical energy into acoustic energy at lowfrequencies, causing problems such as battery drain and overheating. Apotentially even more serious problem is that amplification at lowfrequencies can cause excessive excursion of the loudspeaker's coil,leading to distortion and, in some cases, damage to the loudspeaker.

An alternative is to exploit the psychoacoustic effects of “virtualpitch”. For a simple example to illustrate this effect, consider a pitchwith a fundamental frequency F0 of 100 Hertz (Hz). While the sensationof a 100 Hz pitch can by produced in the human ear by playing a puretone of 100 Hz, musical instruments and human vocal cords usuallyproduce this sensation using a set of tones with a complex harmonicstructure, such as 100 Hz, 200 Hz, 300 Hz, etc., which can also providea fuller (and differentiated) sound quality. What is more interesting isthat the tone at the fundamental frequency of 100 Hz is not necessaryfor people to have the sensation of hearing a 100 Hz pitch. Even if thetone of 100 Hz is missing, a set of harmonic tones at 200 Hz, 300 Hz,400 Hz, etc., can still produce the sensation of a 100 Hz pitch. Thehuman ear apparently can infer the pitch from the harmonic tones alone.This phenomenon is referred to as virtual pitch.

One ramification of the concept of virtual pitch is that we do not needto physically produce a tone at the fundamental frequency F0 in order toproduce the sensation of a pitch at F0. When applied to bass enhancementof small loudspeakers, this means that we do not need to waste energy atlow frequencies where small loudspeakers are not efficient. Instead, wecan produce a similar bass impression by using higher frequency tones,which a loudspeaker is more efficient at producing. As long as anappropriate harmonic structure is provided, the virtual pitch effect canbe strong enough to produce a strong bass sensation. This generalapproach is referred to herein as virtual bass.

Early virtual bass techniques work in the time domain and generallyinvolve the following steps:

1. Extract low-frequency components from the input audio signal using abandpass filter to form a bass signal;

2. Generate higher-order harmonics by feeding the bass signal through anonlinear device;

3. Select a portion of the high-order harmonics (virtual pitch) using abandpass filter; and

4. Add the selected high-order harmonics back into the original signal.

However, the present inventor has recognized that there are problemswith this approach, including the introduction of intermodulationdistortion by the nonlinear device, which can significantly degradeaudio quality.

More recent techniques work in the frequency domain using phasevocoders, e.g., as follows:

1. Use a short time Fourier transform (STFT) to transform the inputaudio signal into the discrete Fourier transform (DFT) domain;

2. Linearly scale up the frequencies of the low-frequency harmonic tonesto frequencies at which the loudspeaker can efficiently produce sound;

3. Use the scaled-up harmonic frequencies to drive sum-of-sinusoidssynthesizers to synthesize a time-domain virtual bass signal; and

4. Add the virtual bass signal back into the original signal.

However, the present inventor has recognized at least one problem withthis approach—that it causes the frequency differences between theharmonic tones also to be scaled up, so the resulting virtual pitchfrequency is higher than it should be. In other words, the resultingvirtual bass typically will be perceived as having a higher pitch thanthe bass portion of the original signal. Even worse, in many cases,particularly where music is involved, the foregoing shift in perceivedpitch will then cause the perceived bass to clash with the otherportions of the audio signal, resulting in an even more severedegradation of the sound quality.

SUMMARY OF THE INVENTION

The present invention addresses the foregoing problems through the useof certain approaches that have been found to produce better results,i.e., more realistic impressions of the original bass portion of anaudio signal.

One specific embodiment of the present invention is directed to anapparatus for processing an audio signal that includes: (a) an inputline that inputs an original audio signal; (b) a transform module thattransforms the original audio signal into a set of frequency components;(c) a filter that extracts a bass portion of such frequency components;(d) an estimator that estimates a fundamental frequency of a bass soundwithin such bass portion; (e) a frequency translator that shifts thebass portion by a frequency that is an integer multiple of thefundamental frequency estimated by the estimator, thereby providing avirtual bass signal; (f) an adder having (i) inputs coupled to theoriginal audio signal and to the virtual bass signal and (ii) an output;and (g) an audio output device coupled to the output of the adder.

Another embodiment is directed to an apparatus for processing an audiosignal, which includes: (a) an input line that inputs an original audiosignal in the time domain; (b) a bass extraction filter that extracts abass portion of the original audio signal, which also is in the timedomain; (c) an estimator that estimates a fundamental frequency of abass sound within the bass portion; (d) a frequency translator thatshifts the bass portion by a positive frequency increment that is aninteger multiple of the fundamental frequency estimated by theestimator, thereby providing a virtual bass signal; (e) an adder having(i) inputs coupled to the original audio signal and to the virtual basssignal and (ii) an output; and (f) an audio output device coupled to theoutput of the adder.

By virtue of each of the foregoing arrangements, it often is possible toobtain better audio output, particularly when an audio signal is beingplayed through a speaker or other audio output device that does notprovide good bass production.

The foregoing summary is intended merely to provide brief description ofcertain aspects of the invention. A more complete understanding of theinvention can be obtained by referring to the claims and the followingdetailed description of the preferred embodiments in connection with theaccompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following disclosure, the invention is described with referenceto the attached drawings. However, it should be understood that thedrawings merely depict certain representative and/or exemplaryembodiments and features of the present invention and are not intendedto limit the scope of the invention in any manner. The following is abrief description of each of the attached drawings.

FIG. 1 is a block diagram of a system for adding virtual bass to anaudio signal in the frequency domain.

FIG. 2 is a block diagram of a system for adding virtual bass to anaudio signal in the time domain.

FIG. 3 is a block diagram of a system for performing single-sideband(SSB) modulation.

DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

This application is related to the commonly assigned U.S. patentapplication titled, “Addition of Virtual Bass in the Time Domain”, ofeven date herewith by the same inventor.

For ease of reference, the present disclosure is divided into sections.The general subject matter of each section is indicated by thatsection's heading. However, such headings are included simply for thepurpose of facilitating readability and are not intended to limit thescope of the invention in any manner whatsoever.

Addition of Virtual Bass in the Frequency Domain.

The first embodiment of the present embodiment, which primarily operatesin the frequency domain, is now discussed in reference to FIG. 1. Asdiscussed in greater detail below, FIG. 1 illustrates a system 5 forprocessing an original input audio signal 10 (typically in digital form,i.e., discrete or sampled in time and discrete or quantized in value),in order to produce an output audio signal 40 that can have less actualbass content than original signal 10, but added “virtual bass”, e.g.,making it more appropriate for speakers or other output devices that arenot very good at producing bass.

Referring to FIG. 1, initially, forward-transform module 12 transformsinput audio signal 10 from the time domain into a frequency-domain(e.g., DFT) representation. Conventional STFT or other conventionalfrequency-transformation techniques can be used within module 12. In thefollowing discussion, it generally is assumed that STFT is used,resulting in a DFT representation, although no loss of generality isintended, and each specific reference herein can be replaced, e.g., withthe foregoing more-generalized language.

The resulting transformed signal is then provided (i.e., coupled) tobass extractor 14 and, optionally, to a high-pass filter 15. Bassextractor 14 extracts the low-frequency portion 16 of the input signal10 from the DFT (or other frequency) coefficients, e.g., using abandpass filter with a pass band (e.g., that portion of the spectrumsubject to not more than 3 dB of attenuation) of[f _(l) ^(b) ,f _(h) ^(b)],   Equation 1where f_(l) ^(b) is the low-end cutoff (−3 dB) frequency, f_(h) ^(b) isthe high-end cutoff frequency, and the foregoing range preferably iscentered where the bass is anticipated to be strong but the intendedloudspeaker or other ultimate output device(s) 42 cannot efficientlyproduce sound. In addition, the bandwidth of bass extractor 14preferably spans enough octaves (e.g., at least 1, 2 or more) so as toextract adequate harmonic structure from the source audio signal 10 forthe purposes indicated below. One representative example of such a passband is [40, 160] Hz. More generally, f_(l) ^(b) preferably is at least10, 15, 20 or 30 Hz, and f_(h) ^(b) preferably is 100-200 Hz.

Typically, bass extractor 14 suppresses the higher-frequency componentsof input signal 10 (and preferably also suppresses very low-frequencycomponents, e.g., those below the range of human hearing), e.g., bydirectly applying a window function, having the desired filtercharacteristics, to the frequency coefficients provided by forward STFTmodule 12. In the preferred embodiments, the purpose of bass extractor14 is to output the bass signal (including its fundamental frequency andat least a portion of its harmonic structure) that is desired to bereplicated as virtual bass (e.g., excluding any very low-frequencyenergy that is below the range of human hearing).

As shown in FIG. 1, extracted bass signal 16 is provided to F0 estimator24 which is used to estimate the fundamental frequency F0 of a basssound (or pitch) within bass signal 16 to which the virtual bass signal25 that is being generated is intended to correspond (i.e., the basssound that virtual bass signal 25 is intended to replace). It is notedthat in the discussion herein, the fundamental frequency isinterchangeably referred to as F0 or F₀. While any F0 detectionalgorithm may be used to provide an estimate of the fundamentalfrequency F0, methods in the frequency domain are preferred in thecurrent embodiment due to the availability of the DFT (or otherfrequency) spectrum. Typically, implicit in such techniques is anidentification of the principal sound or pitch (in this case, theprincipal bass sound or pitch) within the audio signal being processedfor which the fundamental frequency is determined. In this regard, thepresent inventor has discovered that the production of the sensation ofa single bass sound or pitch at any given moment can provide good soundquality. Currently, the preferred approach is as described in XuejingSun, “A Pitch Determination Algorithm Based on Subharmonic-to-HarmonicRatio”, The 6^(th) International Conference of Spoken LanguageProcessing, 2000, pp. 676-679 and/or in Xuejing Sun, “PitchDetermination and Voice Quality Analysis Using Subharmonic-to-HarmonicRatio”, 2002 IEEE International Conference on Acoustics, Speech, andSignal Processing (ICASSP), vol. 1, pp. I-3334-336, 13-17 May 2002.

A smoothing mechanism optionally may be employed to ensure smoothtransitions between audio frames (i.e., smooth variations in F0 fromframe to frame). One such embodiment uses the following first-orderinfinite impulse response (IIR) filter:{circumflex over (F)} ₀(n)=α{circumflex over (F)} ₀(n−1)+(1−α)F ₀(n)where n is the frame number, {circumflex over (F)}₀ is the smoothed F0,and α is the filter coefficient and is related to sampling frequencyf_(s) and time constant τ as

$\alpha = {e^{- \frac{1}{\tau\; f_{s}}}.}$

Bass does not present in an audio signal at all times. When it is absentfor a frame of audio, the virtual bass enhancement mechanism optionallymay be disabled. Turning the virtual bass mechanism on and off in thismanner often will produce a stronger and more desirable bass contrast.For this purpose, most F0 detection algorithms produce a F0 saliencevalue for each audio frame, which typically indicates the strength ofthe pitch harmonic structure in the frame. For example, the sum ofharmonic amplitude (SH) and the subharmonic to harmonic ratio (SHR)mentioned in the above-referenced Sun articles can be used as saliencefunctions when those F0 detection algorithms are used. In the case ofSH, the stronger the harmonic structure, the higher the salience valueis. On the other hand, SHR provides a reverse relationship: the higherthe SHR, the weaker the harmonic structure is.

In any event, the selected F0 salience value can be readily employed toimplement this on/off mechanism. For example, in certain embodiments ifthe F0 salience value in a given frame is lower (or higher, depending onthe nature of the salience value, as indicated in the precedingparagraph) than a specified (e.g., fixed or dynamically set) threshold(or otherwise does not satisfy a specified criterion, e.g., pertainingto a specified threshold), the virtual bass mechanism is turned off(e.g., virtual bass signal 25 is set or forced to 0 for that frame). Asindicated above, there are many potential salience functions, producingdifferent salience values. Each of such salience functions typically hasa number of parameters that can be tuned, so the appropriate thresholdvalue (for turning the virtual bass functionality on and off) for agiven salience value that is to be used preferably is determinedexperimentally. For example, the threshold value may be based onsubjective quality assessments from a test group of individualevaluators. Alternatively, rather than using a fixed threshold valuethat has been determined to be “optimal” in some sense, the user 30 maybe provided with a user interface element that allows the user 30 toadjust the value, e.g., according to his or her individual preferencesand/or based on the nature of the particular sound (or type of sound)that currently is being produced. In still further embodiments, acombination of these approaches is used (e.g., allowing the user 30 toadjust the value when desired and employing a machine-learning algorithmto set the value, based on previous user settings, in those instances inwhich the user 30 has not specified a setting).

The F0 estimate is provided from estimator 24 to translation calculator26, which calculates the frequency translation that frequency translator28 subsequently will use to translate the bass signal 16 (e.g., tofrequencies at which the output device 42 can produce soundefficiently). In order to properly maintain the harmonic structure ofthe bass signal, the frequencies of the translated harmonic tonespreferably are integer multiples of the fundamental frequency F0, so thevalue of frequency translation preferably is:Δ=kF ₀where k is a positive integer, referred to herein as the frequencytranslation multiplier. Using such a frequency translation multiplier, aset of bass harmonic frequencies atF ₀,2F ₀,3F ₀, . . .will be translated (in translator 28) to a set of target harmonicfrequencies atF ₀ +kF ₀,2F ₀ +kF ₀,3F ₀ +kF ₀, . . .In this way, the difference between the target harmonic frequencies isstill F0 and each harmonic frequency is still an integer multiple of F0.Therefore, this set of harmonic frequencies will produce the sensationof the missing virtual pitch. In addition, the translation of thefrequencies surrounding F₀ by the same amount (Δ) often can preserve theoriginal bass quality, from a perceptual standpoint.

The frequency translation multiplier preferably ensures that the basssignal is shifted to frequencies at which the loudspeaker canefficiently produce sound. In this regard, if f_(l) ^(t) denotes thelowest frequency at which the loudspeaker can efficiently produce sound,one such frequency translation multiplier for a bass signal with apassband given by Equation 1 may be determined as:

$\begin{matrix}{{k = {\lceil \frac{f_{l}^{t}}{f_{l}^{b}} \rceil - 1}},} & {{Equation}\mspace{14mu} 2}\end{matrix}$where ┌x┐ is the ceiling function which returns the smallest integerthat is greater than or equal to x. For the range of the extracted basssignal 16 (which is assumed to include F0) given in Equation 1, thecorresponding range of the translated (frequency-shifted) F0 will thenbe:[f _(l) ^(b)(k+1),f _(h) ^(b)(k+1)].   Equation 3

When the estimated F0 is on the high end of the range given in Equation1, the multiplier k specified above may cause the bass signal to betranslated to a very high frequency range, leading to a less desirablebass perception. This problem may be alleviated by instead using thefollowing multiplier:

$\begin{matrix}{k = {\lceil \frac{f_{l}^{t}}{F_{0}} \rceil - 1.}} & {{Equation}\mspace{14mu} 4}\end{matrix}$This multiplier is a function of the estimated F0 and, therefore, variesfrom frame to frame as the estimated F0 changes. In order to limit theeffects of a discontinuity when the estimated F0 changes around a valuewhich leads to f_(l) ^(t)/F₀ being an integer, preferably a one-octaveF0 range at the top of the range given in Equation 1 is set as the rangefor the allowed F0 estimate, i.e., so that the F0 estimate isconstrained to be within the range:

$\begin{matrix}{\lbrack {{\frac{1}{2}f_{h}^{b}},f_{h}^{b}} \rbrack,} & {{Equation}\mspace{14mu} 5}\end{matrix}$and any initial F0 estimate is shifted into this range by raising itsoctave. Then, the translation multiplier may be obtained as:

$\begin{matrix}{{k = {\lceil \frac{f_{l}^{t} + {\frac{1}{2}f_{h}^{b}} - f_{l}^{b}}{\frac{1}{2}f_{h}^{b}} \rceil - 1}},} & {{Equation}\mspace{14mu} 6}\end{matrix}$which is a fixed value. Because this modified F0 estimate is confined tothe range specified in Equation 5, the corresponding range of thetranslated (shifted) F0 is

$\lbrack {{\frac{1}{2}{f_{h}^{b}( {k + 1} )}},{f_{h}^{b}( {k + 1} )}} \rbrack,$which is significantly smaller than the range specified by Equation 3.

Another advantage of defining the multiplier k as set forth in Equation6 is that it renders irrelevant the problem of octave error, which is acommon problem for most F0 detection algorithms. In this regard, it isnoted that F0 detection algorithms tend to produce an estimate that isone or more octaves higher or lower than the real one. Such an errorwould cause a bass signal to be translated to dramatically differentfrequencies if Equation 2 or Equation 4 is used. This problem becomesirrelevant when Equation 6 is used because the estimated F0 is convertedto the range of Equation 5.

Translation calculator 26 provides the translation information (e.g.,either Δ alone, or k together with F₀) to frequency translator 28, whichpreferably translates (or shifts) the entire extracted bass signal 16 bythe fixed frequency increase Δ (e.g., to frequencies where theloudspeaker or other output device(s) 42 can produce sound efficiently),while ensuring that the harmonic structure of the bass signal 16 is leftunchanged. The frequency representation of the virtual bass signal V(f,n) of the n-th STFT frame can be obtained from the frequencyrepresentation of the bass signal 16, B(f,n), e.g., asV(f,n)=B(f−Δ,n)e ^(j2πΔnM),where M is the block size of the STFT. The phase adjustment indicatedabove is desirable to ensure smooth phase transitions between successiveSTFT frames. See, e.g., J. Laroche and M. Dolson, “New phase-vocodertechniques for real-time pitch shifting, chorusing, harmonizing, andother exotic audio modifications,” Journal of the Audio EngineeringSociety, 47.11 (1999): pp. 928-936.

It is noted that in the presently preferred embodiment, F0 isconstrained to be a frequency corresponding to a transform frequency(e.g., DFT) bin and, therefore, Δ is an integer multiple of thefrequency bin width. For the present purposes, adoption of such aconstraint has been found to significantly simplify the requiredprocessing without causing any substantial degradation in quality.However, it is possible to accommodate the fractional case, and systemsand processes that do so are intended to be included within the scope ofthe present invention. The article by Laroche and Dolson cited in thepreceding paragraph discusses an approach along these lines.

Because human loudness perception is less sensitive at low frequencies,absent adjustment, the virtual bass signal 25 that is to be added insystem 5 (which consists of a set of higher frequencies) typically wouldsound (i.e., be perceived as being) much louder than the actual bassthat is present in the original signal 10. However, it is preferable tomake the added virtual bass sound as loud as the original bass so thatthe perceived loudness balance is maintained. Toward this end, the mainpurpose of loudness control module 29 is to estimate the change in theperceived loudness level of the virtual bass signal 25, as compared tothe original bass in input signal 10, and then use that information togenerate a scale factor that is intended to equalize the two, i.e., toestimate the optimal volume adjustment for the virtual bass signal 25 sothat the virtual bass blends well with the original audio signal 10. Inaddition, in certain embodiments, system 5 presents a user interfaceallows a user 30 to adjust a setting that results in a modification tothis scale factor in order to suit the user 30's preferences (e.g.,increased or decreased bass sensation).

Preferably, loudness control module 29 first estimates the soundpressure level (SPL) or the power of the extracted bass signal 16. Oneapproach to doing so is to calculate the following average of power overthe pass band, e.g.:

$L_{p}^{B} = {10\;\log_{10}\frac{1}{H - L + 1}{\sum\limits_{n = L}^{H}\;{X_{n}}^{2}}}$where X_(n) is the n-th DFT coefficient, L and H are the lowest andhighest, respectively, DFT bin numbers within bass signal 16. Inaddition, loudness control module 29 preferably identifies arepresentative or nominal frequency within the extracted bass signal 16.The geometric mean may be used to calculate this representative ornominal frequency for the original bass signal 16, e.g. as:

$f_{B} = ( {\prod\limits_{f_{n} = f_{l}^{b}}^{f_{h}^{b}}\; f_{n}} )^{\frac{1}{H - L + 1}}$where f_(n) is the frequency of the n-th DFT bin. This representative ornominal frequency and power can then be plugged into equation (2) of ISO226:2003 to obtain the loudness level L_(N) of the original bass signal16.

Similarly, the representative or nominal frequency for the correspondingvirtual bass signal 25 may be calculated as follows:

$f_{V} = {( {{\prod\limits_{f_{n} = f_{l}^{b}}^{f_{h}^{b}}\; f_{n}} + {kF}_{0}} )^{\frac{1}{H - L + 1}}.}$This representative or nominal frequency f_(V) and the loudness levelL_(N) can then be plugged into equation (1) of ISO 226:2003 to obtainthe target SPL, L_(p) ^(V), which can then be converted into the targetscale factor s as:s=10^(0.05L) ^(p) ^(V) .This scale factor s, either with or without modification by a user 30(e.g., as discussed above), is then provided to multiplier 32, alongwith the virtual bass signal 25, in order to produce the desiredvolume-adjusted virtual bass signal 25′. The combination of loudnesscontrol module 29 and multiplier 32 collectively can be referred toherein as a “loudness controller” or a “loudness equalizer”. Also,although ISO 226:2003 is referenced herein, any other (e.g., similar)equal-loudness-level data set instead may be used.

As noted above, the frequency-domain transformed version of input signal10 also may be provided to an optional high-pass filter 15. The purposeof high-pass filter 15 (if provided) is to suppress the entire lowerportion of the spectrum that cannot be efficiently reproduced by theintended output device(s) 42. For example, frequencies below a specifiedfrequency (e.g., having a value of 50-200 Hz) might be filtered out byhigh-pass filter 15. It should be noted that, particularly because it ispreferable for bass extractor 14 to extract at least a portion of theharmonic structure of the bass pitch (or sound), there might be overlapbetween the frequency spectrum of bass signal 16 and the spectrum thathigh-pass filter 15 passes through. Similar to bass extractor 14,high-pass filter 15 (if provided) typically performs its filteringoperation (i.e., in this case, suppressing the low-frequency componentsof input signal 10), e.g., by directly applying a window function withthe desired filter characteristics to the frequency coefficientsprovided by transform module 12. As previously indicated, a high-passfilter 15 can reduce the amount of energy that, e.g., otherwise would bewasted in small loudspeakers or might result in other negative effects,but it is neither an essential nor necessary part of a virtual-basssystem, process or approach according to the present invention.

In adder 35, the frequency-domain virtual bass signal 25′ is summed withthe frequency-transformed and potentially high-pass filtered inputsignal. Finally, the backward transformation (i.e., the reverse of thetransformation performed in module 12) is performed in module 36 inorder to convert the composite signal back into the time domain. Theresulting output signal 40 typically is subject to additional processing(e.g., digital-to-analog conversion, loudness compensation, such asdiscussed in commonly assigned U.S. patent application Ser. No.14/852,576, filed Sep. 13, 2015, which is incorporated by referenceherein as though set forth herein in full, and/or amplification) beforebeing provided to speaker or other output device(s) 42. Alternatively,any or all of such additional processing may have been performed oninput signal 10 prior to providing it to system 5.

Addition of Virtual Bass in the Time Domain.

An alternate embodiment of the present embodiment, which operatesentirely in the time domain, is now discussed primarily in reference toFIG. 2. As discussed in greater detail below, FIG. 2 illustrates asystem 105 for processing an original input audio signal 10 (typicallyin digital form), in order to produce an output audio signal 140 that,as in system 5 discussed above, can have less actual bass content thanoriginal signal 10, but added “virtual bass”, e.g., making it moreappropriate for speakers or other output devices that are not very goodat producing bass.

Referring to FIG. 2, initially, bass extractor 114 extracts thelow-frequency portion of the input signal 10 (e.g., other than a verylow-frequency portion that is below the range of human hearing),preferably using a bandpass filter. Like bass extractor 14, the passbandof bass extractor 114 preferably is as specified in Equation 1, and thecharacteristics of bass extractor 114 are the same as those of bassextractor 14, except that bass extractor 114 operates in the timedomain. Conventional finite impulse response (FIR) or IIR filters may beused for bass extractor 114. The extracted bass signal (or bass portion)116 is provided to F0 estimator 124.

While any F0 detection algorithm may be used by F0 estimator 124 toprovide an estimate of the fundamental frequency F0, in order to avoidadditional complexity, methods in the time domain are preferred in thecurrent embodiment. The preferred F0 detection algorithm examines aspecified number of audio samples, referred to as the integrationwindow, having a size that preferably is at least twice the periodcorresponding to the minimum expected F0. After the F0 value isobtained, the audio samples preferably are advanced by a number ofsamples, referred to as a frame, having a size that preferably is afraction of (i.e., smaller than) that of the integration window. If theF0 estimate is updated frequently (i.e., the frame size is smallcompared with the integration window), a simple F0 detection method,such as the zero-crossing rate (ZCR) method, preferably is used in orderto maintain a reasonable computation load. On the other hand, if the F0estimate is updated infrequently, more sophisticated methods, such asthe YIN estimation method, as discussed, e.g., in Kawahara H. deCheveigné, “YIN, a fundamental frequency estimator for speech andmusic”, J Acoust Soc Am., April 2002, 111(4):1917-30, can be used toprovide a more reliable and accurate F0 estimate. In addition, as withF0 estimator 24, F0 estimator 124 preferably also employs a (e.g.,similar or identical) smoothing mechanism to smooth variations in the F0estimate between audio frames and/or a salience measure estimate andcorresponding threshold (or similar or related criterion) to turn thevirtual bass mechanism on and off within individual frames.

The F0 estimate generated by estimator 124 is provided to translationcalculator 126, which preferably is similar or identical to translationcalculator 26, discussed above, and the same considerations generallyapply. The output of translation calculator 126 (e.g., either Δ alone,or k together with F₀) is then provided to frequency translator 128 andloudness control module 129.

Frequency translator 128 translates (or frequency shifts) the entireextracted bass signal 116 by the calculated positive frequency incrementΔ, e.g., to frequencies where the loudspeaker can produce soundefficiently, while ensuring that the harmonic structure of the basssignal is left unchanged. A simple way to implement frequency translator128 is to use double-sideband (DSB) modulation, e.g., as follows:v(n)=b(n)cos(2πf _(c) n),where n is the sample index, f_(c) is the carrier frequency (e.g., Δ),b(n) is the extracted bass signal 116, and v(n) is the resulting virtualbass signal 125, respectively. Using the modulation theorem of theFourier transform, we obtain the spectrum of the virtual bass signal,V(f), as:

${{V(f)} = {\frac{1}{2}\lbrack {{B( {f - f_{c}} )} + {B( {f + f_{c}} )}} \rbrack}},$where B(f) is the spectrum of the extracted bass signal 116. Asindicated above, the virtual bass spectrum consists of two sidebands, orfrequency-shifted copies of the bass spectrum, on either side of thecarrier frequency, with the lower sideband being a frequency-flipped ormirrored copy of the bass spectrum. If the carrier frequency is set tobe a multiple of the estimated F0, both sidebands can still maintain avalid harmonic structure, so the virtual bass spectrum B(f) constitutesa valid virtual signal.

There are other options for selecting the carrier frequency f_(c). Oneis to select such a value that both the lower and higher sidebands aretranslated to the frequency range where the loudspeaker can efficientlyproduce sound. This approach would result in there being twofrequency-shifted copies of the bass spectrum in the virtual bass signal125: the lower sideband and the upper sideband, so the timber of thevirtual bass signal would be significantly altered. Another option is toselect the carrier frequency f_(c) to be such a value that only theupper sideband is translated to the frequency range where theloudspeaker can efficiently produce sound. Because the fundamental bassfrequency is F0, such a carrier frequency preferably is selected as:f _(c) =kf ₀,which ensures that the lower sideband is below the frequencies where theloudspeaker can efficiently produce sound, so the effect of the lowersideband on timber is limited. However, this lower sideband typicallydoes produce excessive heat and coil excursion and, therefore, should besuppressed.

When the lower sideband is suppressed, the resulting frequencytranslation approach is referred to as single-sideband (SSB) modulation.One approach to SSB modulation is to employ a bandpass filter to filterout the lower sideband. This filter preferably has a bandwidth that issimilar or identical to that of the extracted bass signal 116, but itscenter frequency preferably varies with the estimated F0. Due to thevarying center frequency, a FIR filter such as the following truncatedideal bandpass filter preferably is used:

${h(n)} = \{ {\begin{matrix}{{\frac{\sin\lbrack {2\;\pi\;{f_{h}( {n - M} )}} \rbrack}{\pi( {n - M} )} - \frac{\sin\lbrack {2\;\pi\;{f_{l}( {n - M} )}} \rbrack}{\pi( {n - M} )}},} & {n \neq M} \\{{2( {f_{h} - f_{l}} )},} & {n = M}\end{matrix},} $where N is the length of the filter, M=N/2, and f_(l) and f_(h) arefrequencies corresponding to the low and high edges, respectively, ofthe passband.

A currently more preferred approach to SSB modulation is to use theHilbert transform to create an analytic signal from the extracted basssignal 116, translate that analytic signal to the desired frequency, andtake its real part. One algorithm to efficiently implement this processis illustrated in FIG. 3. The Hilbert transform may be approximated by aFIR filter, which can be designed using the Parks-McClellan algorithm(e.g., as discussed in David Ernesto Troncoso Romero and GordanaJovanovic Dolecek, “Digital FIR Hilbert Transformers: Fundamentals andEfficient Design Methods”, chapter 19 in “MATLAB—A Fundamental Tool forScientific Computing and Engineering Applications—Volume 1”, Prof.Vasilios Katsikis (Ed.), Intech, ISBN: 978-953-51-0750-7, InTech, DOI:10.5772/46451, pp. 445-482 (2012). For implementation using IIR filters,see, e.g., Scott Wardle, “A Hilbert transformer frequency shifter foraudio,” First Workshop on Digital Audio Effects DAFx, 1998.

As shown in FIG. 2, the extracted bass signal 116 and the output oftranslation calculator 126 (e.g., either Δ alone, or k together with F₀)are provided to loudness control module 129, which preferably providesfunctionality similar to loudness control module 29, discussed above,but operates in the time domain. For example, in this embodiment asliding average of power values within extracted bass signal 116 may becalculated as follows:P(n)=Σ_(k=0) ^(N-1) x ²(n−k),   Equation 7where x(n) is the input sample value and N is the block size. A simplerembodiment is to use a low-order IIR filter, such as the followingfirst-order IIR filter:P(n)=αP(n−1)+(1−α)x ²(n),   Equation 8where α is the filter coefficient and is related to sampling frequencyf_(s) and time constant τ asα=e ^(−1/(τf) ^(s) ⁾.The representative or nominal frequency for the bass signal may becalculated, e.g., using either the arithmetic mean of the limit given inEquation 1 or the following geometric mean:f _(B)=√{square root over (f _(l) ^(b) f _(h) ^(b))}.This representative or nominal frequency and the calculated bass power(e.g., as given in Equation 7 or Equation 8) can then be plugged intoequation (2) of ISO 226:2003 to obtain its loudness level L_(N).

The frequency range of the virtual bass signal 125 is[f _(l) ^(b) +kF ₀ ,f _(h) ^(b) +kF ₀].Therefore, the representative or nominal frequency for the virtual basssignal 125 may be calculated as the arithmetic mean of the limit aboveor as its geometric mean, e.g.:f _(V)=√{square root over ((f _(l) ^(b) +kF ₀)(f _(h) ^(b) +kF ₀))}.This representative or nominal frequency and the loudness level L_(N)can then be plugged into equation (1) of ISO 226:2003 to obtain thetarget SPL L_(p) ^(V), which can be further converted into the scalefactor, e.g., as:s=10^(0.05L) ^(p) ^(V).As in the preceding embodiment, this scale factor s preferably may bemodified by a user 30. With or without such modification, scale factor sis then provided to multiplier 132, along with the virtual bass signal125, in order to produce the desired volume-adjusted virtual bass signal125′. The combination of loudness control module 129 and multiplier 132collectively can be referred to herein as a “loudness controller” or a“loudness equalizer”.

Input signal 10 also may be provided to an optional high-pass filter115. Similar to high-pass filter 15 (if provided), filter 115 preferablysuppresses the entire lower portion of the spectrum of the input audiosignal 10 that cannot be efficiently reproduced by the intended outputdevice(s) 42. The preferred frequency characteristics of filter 115 (ifprovided) the same as those provided above for filter 15. However,filter 115 (if provided) operates in the time domain (e.g., implementedas a FIR or IIR filter).

Following filter 115 (if provided), a delay element 134 delays thepotentially filtered original audio signal to time-align it to thesynthesized virtual bass signal 125′. Thereafter, the two signals aresummed in adder 135. The resulting output signal 140 typically issubject to additional processing (e.g., as discussed above in relationto system 5) before being provided to speaker or other output device(s)42. Alternatively, as with system 5, any or all of such additionalprocessing may have been performed on input signal 10 prior to providingit to system 105.

System Environment.

Generally speaking, except where clearly indicated otherwise, all of thesystems, methods, functionality and techniques described herein can bepracticed with the use of one or more programmable general-purposecomputing devices. Such devices (e.g., including any of the electronicdevices mentioned herein) typically will include, for example, at leastsome of the following components coupled to each other, e.g., via acommon bus: (1) one or more central processing units (CPUs); (2)read-only memory (ROM); (3) random access memory (RAM); (4) otherintegrated or attached storage devices; (5) input/output software andcircuitry for interfacing with other devices (e.g., using a hardwiredconnection, such as a serial port, a parallel port, a USB connection ora FireWire connection, or using a wireless protocol, such asradio-frequency identification (RFID), any other near-fieldcommunication (NFC) protocol, Bluetooth or a 802.11 protocol); (6)software and circuitry for connecting to one or more networks, e.g.,using a hardwired connection such as an Ethernet card or a wirelessprotocol, such as code division multiple access (CDMA), global systemfor mobile communications (GSM), Bluetooth, a 802.11 protocol, or anyother cellular-based or non-cellular-based system, which networks, inturn, in many embodiments of the invention, connect to the Internet orto any other networks; (7) a display (such as a cathode ray tubedisplay, a liquid crystal display, an organic light-emitting display, apolymeric light-emitting display or any other thin-film display); (8)other output devices (such as one or more speakers, a headphone set, alaser or other light projector and/or a printer); (9) one or more inputdevices (such as a mouse, one or more physical switches or variablecontrols, a touchpad, tablet, touch-sensitive display or other pointingdevice, a keyboard, a keypad, a microphone and/or a camera or scanner);(10) a mass storage unit (such as a hard disk drive or a solid-statedrive); (11) a real-time clock; (12) a removable storage read/writedevice (such as a flash drive, any other portable drive that utilizessemiconductor memory, a magnetic disk, a magnetic tape, an opto-magneticdisk, an optical disk, or the like); and/or (13) a modem (e.g., forsending faxes or for connecting to the Internet or to any other computernetwork). In operation, the process steps to implement the above methodsand functionality, to the extent performed by such a general-purposecomputer, typically initially are stored in mass storage (e.g., a harddisk or solid-state drive), are downloaded into RAM, and then areexecuted by the CPU out of RAM. However, in some cases the process stepsinitially are stored in RAM or ROM and/or are directly executed out ofmass storage.

Suitable general-purpose programmable devices for use in implementingthe present invention may be obtained from various vendors. In thevarious embodiments, different types of devices are used depending uponthe size and complexity of the tasks. Such devices can include, e.g.,mainframe computers, multiprocessor computers, one or more server boxes,workstations, personal (e.g., desktop, laptop, tablet or slate)computers and/or even smaller computers, such as personal digitalassistants (PDAs), wireless telephones (e.g., smartphones) or any otherprogrammable appliance or device, whether stand-alone, hard-wired into anetwork or wirelessly connected to a network.

In addition, although general-purpose programmable devices have beendescribed above, in alternate embodiments one or more special-purposeprocessors or computers instead (or in addition) are used. In general,it should be noted that, except as expressly noted otherwise, any of thefunctionality described above can be implemented by a general-purposeprocessor executing software and/or firmware, by dedicated (e.g.,logic-based) hardware, or any combination of these approaches, with theparticular implementation being selected based on known engineeringtradeoffs. More specifically, where any process and/or functionalitydescribed above is implemented in a fixed, predetermined and/or logicalmanner, it can be accomplished by a processor executing programming(e.g., software or firmware), an appropriate arrangement of logiccomponents (hardware), or any combination of the two, as will be readilyappreciated by those skilled in the art. In other words, it iswell-understood how to convert logical and/or arithmetic operations intoinstructions for performing such operations within a processor and/orinto logic gate configurations for performing such operations; in fact,compilers typically are available for both kinds of conversions.

It should be understood that the present invention also relates tomachine-readable tangible (or non-transitory) media on which are storedsoftware or firmware program instructions (i.e., computer-executableprocess instructions) for performing the methods and functionality ofthis invention. Such media include, by way of example, magnetic disks,magnetic tape, optically readable media such as CDs and DVDs, orsemiconductor memory such as various types of memory cards, USB flashmemory devices, solid-state drives, etc. In each case, the medium maytake the form of a portable item such as a miniature disk drive or asmall disk, diskette, cassette, cartridge, card, stick etc., or it maytake the form of a relatively larger or less-mobile item such as a harddisk drive, ROM or RAM provided in a computer or other device. As usedherein, unless clearly noted otherwise, references tocomputer-executable process steps stored on a computer-readable ormachine-readable medium are intended to encompass situations in whichsuch process steps are stored on a single medium, as well as situationsin which such process steps are stored across multiple media.

The foregoing description primarily emphasizes electronic computers anddevices. However, it should be understood that any other computing orother type of device instead may be used, such as a device utilizing anycombination of electronic, optical, biological and chemical processingthat is capable of performing basic logical and/or arithmeticoperations.

In addition, where the present disclosure refers to a processor,computer, server, server device, computer-readable medium or otherstorage device, client device, or any other kind of apparatus or device,such references should be understood as encompassing the use of pluralsuch processors, computers, servers, server devices, computer-readablemedia or other storage devices, client devices, or any other suchapparatuses or devices, except to the extent clearly indicatedotherwise. For instance, a server generally can (and often will) beimplemented using a single device or a cluster of server devices (eitherlocal or geographically dispersed), e.g., with appropriate loadbalancing. Similarly, a server device and a client device often willcooperate in executing the process steps of a complete method, e.g.,with each such device having its own storage device(s) storing a portionof such process steps and its own processor(s) executing those processsteps.

As used herein, the term “coupled”, or any other form of the word, isintended to mean either directly connected or connected through one ormore other elements or processing blocks. In the drawings and/or thediscussions of them, where individual steps, modules or processingblocks are shown and/or discussed as being directly connected to eachother, such connections should be understood as couplings, which mayinclude additional elements and/or processing blocks. Unless otherwiseexpressly and specifically stated otherwise herein to the contrary,references to a signal herein mean any processed or unprocessed versionof the signal. That is, specific processing steps discussed and/orclaimed herein are not intended to be exclusive; rather, intermediateprocessing may be performed between any two processing steps expresslydiscussed or claimed herein.

Additional Considerations.

In the preceding discussion, the terms “operators”, “operations”,“functions” and similar terms can refer to method steps or hardwarecomponents, depending upon the particular implementation/embodiment.

Unless clearly indicated to the contrary, words such as “optimal”,“optimize”, “minimize”, “best”, as well as similar words and other wordsand suffixes denoting comparison, in the above discussion are not usedin their absolute sense. Instead, such terms ordinarily are intended tobe understood in light of any other potential constraints, such asuser-specified constraints and objectives, as well as cost andprocessing constraints.

References herein to a “criterion”, “multiple criteria”, “condition”,“conditions” or similar words which are intended to trigger, limit,filter or otherwise affect processing steps, other actions, the subjectsof processing steps or actions, or any other activity or data, areintended to mean “one or more”, irrespective of whether the singular orthe plural form has been used. For instance, any criterion or conditioncan include any combination (e.g., Boolean combination) of actions,events and/or occurrences (i.e., a multi-part criterion or condition).

Similarly, in the discussion above, functionality sometimes is ascribedto a particular module or component. However, functionality generallymay be redistributed as desired among any different modules orcomponents, in some cases completely obviating the need for a particularcomponent or module and/or requiring the addition of new components ormodules. The precise distribution of functionality preferably is madeaccording to known engineering tradeoffs, with reference to the specificembodiment of the invention, as will be understood by those skilled inthe art.

In the discussions above, the words “include”, “includes”, “including”,and all other forms of the word should not be understood as limiting,but rather any specific items following such words should be understoodas being merely exemplary.

Several different embodiments of the present invention are describedabove [and in the documents incorporated by reference herein, with eachsuch embodiment described as including certain features. However, it isintended that the features described in connection with the discussionof any single embodiment are not limited to that embodiment but may beincluded and/or arranged in various combinations in any of the otherembodiments as well, as will be understood by those skilled in the art.

Thus, although the present invention has been described in detail withregard to the exemplary embodiments thereof and accompanying drawings,it should be apparent to those skilled in the art that variousadaptations and modifications of the present invention may beaccomplished without departing from the spirit and the scope of theinvention. Accordingly, the invention is not limited to the preciseembodiments shown in the drawings and described above. Rather, it isintended that all such variations not departing from the spirit of theinvention are to be considered as within the scope thereof as limitedsolely by the claims appended hereto.

What is claimed is:
 1. An apparatus for processing an audio signal,comprising: (a) an input line that inputs an original audio signal; (b)a transform module that transforms the original audio signal into a setof frequency components; (c) a bass extraction filter that extracts abass portion of said frequency components; (d) an estimator thatestimates a fundamental frequency of a bass sound within said bassportion; (e) a frequency translator that shifts the bass portion by apositive frequency increment that is an integer multiple of thefundamental frequency estimated by said estimator, thereby providing avirtual bass signal; (f) an adder having (i) inputs coupled to saidoriginal audio signal and to said virtual bass signal and (ii) anoutput; and (g) an audio output device coupled to the output of saidadder, wherein said bass extraction filter, estimator, frequencytranslator and adder operate on discrete frames of the original audiosignal, and further comprising a smoothing filter that adjusts thefundamental frequency in individual ones of said discrete frames tosmooth changes in the fundamental frequency across said frames.
 2. Anapparatus according to claim 1, wherein said bass extraction filter is abandpass filter having a low-end cutoff frequency of at least 15 Hz. 3.An apparatus according to claim 1, wherein said bass extraction filteris a bandpass filter having a passband of at least 1 octave.
 4. Anapparatus according to claim 1, wherein said bass extraction filter is abandpass filter having a passband of at least 2 octaves.
 5. An apparatusaccording to claim 1, further comprising a loudness controller thatadjusts a strength of said virtual bass signal based on a first estimateof a perceived loudness of said bass portion and a second estimate of aperceived loudness of said virtual bass signal.
 6. An apparatusaccording to claim 5, wherein the first estimate is based on an estimateof at least one of a sound pressure level (SPL) or a power of the bassportion.
 7. An apparatus for processing an audio signal, comprising: (a)an input line that inputs an original audio signal; (b) a transformmodule that transforms the original audio signal into a set of frequencycomponents; (c) a bass extraction filter that extracts a bass portion ofsaid frequency components; (d) an estimator that estimates a fundamentalfrequency of a bass sound within said bass portion; (e) a frequencytranslator that shifts the bass portion by a positive frequencyincrement that is an integer multiple of the fundamental frequencyestimated by said estimator, thereby providing a virtual bass signal;(f) an adder having (i) inputs coupled to said original audio signal andto said virtual bass signal and (ii) an output; (g) an audio outputdevice coupled to the output of said adder; and (h) a loudnesscontroller that adjusts a strength of said virtual bass signal based ona first estimate of a perceived loudness of said bass portion and asecond estimate of a perceived loudness of said virtual bass signal,wherein the loudness controller determines a scale factor based on arepresentative frequency for the bass portion, a strength of the bassportion, a representative frequency for the virtual bass signal and anequal-loudness-level data set.
 8. An apparatus according to claim 7,wherein the representative frequency for the bass portion is determinedas a geometric mean across the bass portion.
 9. An apparatus accordingto claim 1, wherein the transform module performs a short time Fouriertransform (STFT).
 10. An apparatus for processing an audio signal,comprising: (a) an input line that inputs an original audio signal; (b)a transform module that transforms the original audio signal into a setof frequency components; (c) a bass extraction filter that extracts abass portion of said frequency components; (d) an estimator thatestimates a fundamental frequency of a bass sound within said bassportion; (e) a frequency translator that shifts the bass portion by apositive frequency increment that is an integer multiple of thefundamental frequency estimated by said estimator, thereby providing avirtual bass signal; (f) an adder having (i) inputs coupled to saidoriginal audio signal and to said virtual bass signal and (ii) anoutput; and (g) an audio output device coupled to the output of saidadder, wherein said estimator also estimates a salience value of saidbass sound, and wherein said virtual bass signal is forced to 0 if saidsalience value does not satisfy a specified criterion.
 11. An apparatusaccording to claim 1, wherein the fundamental frequency of said basssound is constrained to fall within a one-octave range.
 12. An apparatusaccording to claim 1, wherein the fundamental frequency is constrainedto be one of the frequency components in the set provided by thetransform module.
 13. An apparatus according to claim 1, furthercomprising a backward transform module, having an input coupled to anoutput of said adder and an output coupled to an input of the audiooutput device, that performs a reverse of the transform performed by thetransform module.
 14. An apparatus according to claim 10, wherein saidbass extraction filter, estimator, frequency translator and adderoperate on discrete frames of the original audio signal, and furthercomprising a smoothing filter that adjusts the fundamental frequency inindividual ones of said discrete frames to smooth changes in thefundamental frequency across said frames.
 15. An apparatus according toclaim 1, wherein said smoothing filter implements a smoothing function{circumflex over (F)}₀(n)=α{circumflex over (F)}₀(n−1)+(1−α)F₀(n), wheren is a number of the current frame number, {circumflex over (F)}₀ is asmoothed version of F₀, and α is a filter coefficient.
 16. An apparatusfor processing an audio signal, comprising: (a) an input line thatinputs an original audio signal; (b) a transform module that transformsthe original audio signal into a set of frequency components; (c) a bassextraction filter that extracts a bass portion of said frequencycomponents; (d) an estimator that estimates a fundamental frequency of abass sound within said bass portion; (e) a frequency translator thatshifts the bass portion by a positive frequency increment that is aninteger multiple of the fundamental frequency estimated by saidestimator, thereby providing a virtual bass signal; (f) an adder having(i) inputs coupled to said original audio signal and to said virtualbass signal and (ii) an output; and (g) an audio output device coupledto the output of said adder, wherein the integer multiple is determinedas ${k = {\lceil \frac{f_{l}^{t}}{f_{l}^{b}} \rceil - 1}},$where k is the integer multiple, f_(l) ^(b) is a low- and cut offfrequency of a bandpass filter that functions as the bass extractionfilter, f_(l) ^(t) denotes a designated lowest acceptable frequency, and┌x┐ is a ceiling function which returns a smallest integer that is notless than x.
 17. An apparatus for processing an audio signal,comprising: (a) an input line that inputs an original audio signal; (b)a transform module that transforms the original audio signal into a setof frequency components; (c) a bass extraction filter that extracts abass portion of said frequency components; (d) an estimator thatestimates a fundamental frequency of a bass sound within said bassportion; (e) a frequency translator that shifts the bass portion by apositive frequency increment that is an integer multiple of thefundamental frequency estimated by said estimator, thereby providing avirtual bass signal; (f) an adder having (i) inputs coupled to saidoriginal audio signal and to said virtual bass signal and (ii) anoutput; and (g) an audio output device coupled to the output of saidadder, wherein the integer multiple is determined as${k = {\lceil \frac{f_{l}^{t}}{F_{0}} \rceil - 1}},$ where kis the integer multiple, F₀ is the fundamental frequency, f_(l) ^(t)denotes a designated lowest acceptable frequency, and ┌x┐ is a ceilingfunction which returns a smallest integer that is not less than x. 18.An apparatus for processing an audio signal, comprising: (a) an inputline that inputs an original audio signal; (b) a transform module thattransforms the original audio signal into a set of frequency components;(c) a bass extraction filter that extracts a bass portion of saidfrequency components; (d) an estimator that estimates a fundamentalfrequency of a bass sound within said bass portion; (e) a frequencytranslator that shifts the bass portion by a positive frequencyincrement that is an integer multiple of the fundamental frequencyestimated by said estimator, thereby providing a virtual bass signal;(f) an adder having (i) inputs coupled to said original audio signal andto said virtual bass signal and (ii) an output; and (g) an audio outputdevice coupled to the output of said adder, wherein the integer multipleis determined as${k = {\lceil \frac{f_{l}^{t} + {\frac{1}{2}f_{h}^{b}} - f_{l}^{b}}{\frac{1}{2}f_{h}^{b}} \rceil - 1}},$where k is the integer multiple, f_(l) ^(t) denotes a designated lowestacceptable frequency, f_(l) ^(b) is a low-end cutoff frequency of abandpass filter that functions as the bass extraction filter, f_(h) ^(b)is a high-end cutoff frequency of the bass extraction filter, and ┌x┐ isa ceiling function which returns a smallest integer that is not lessthan x.
 19. An apparatus according to claim 1, further comprising ahigh-pass filter that suppresses frequencies within said original audiosignal that are not capable of being efficiently converted into sound bysaid audio output device.
 20. An apparatus according to claim 19,wherein said high-pass filter is coupled to an output of said transformmodule and operates on said set of frequency components.
 21. Anapparatus according to claim 10, wherein said bass extraction filter isa bandpass filter having a low-end cutoff frequency of at least 15 Hz.22. An apparatus according to claim 10, wherein said bass extractionfilter is a bandpass filter having a passband of at least 1 octave. 23.An apparatus according to claim 10, wherein said bass extraction filteris a bandpass filter having a passband of at least 2 octaves.
 24. Anapparatus according to claim 10, further comprising a loudnesscontroller that adjusts a strength of said virtual bass signal based ona first estimate of a perceived loudness of said bass portion and asecond estimate of a perceived loudness of said virtual bass signal. 25.An apparatus according to claim 24, wherein the first estimate is basedon an estimate of at least one of a sound pressure level (SPL) or apower of the bass portion.
 26. An apparatus according to claim 10,wherein the fundamental frequency of said bass sound is constrained tofall within a one-octave range.
 27. An apparatus according to claim 10,wherein the fundamental frequency is constrained to be one of thefrequency components in the set provided by the transform module.
 28. Anapparatus according to claim 10, further comprising a high-pass filterthat suppresses frequencies within said original audio signal that arenot capable of being efficiently converted into sound by said audiooutput device.
 29. An apparatus according to claim 28, wherein saidhigh-pass filter is coupled to an output of said transform module andoperates on said set of frequency components.